A183382 Half the number of n X 3 binary arrays with no element equal to a strict majority of its king-move neighbors.

1, 5, 11, 29, 89, 245, 669, 1891, 5297, 14753, 41267, 115455, 322661, 902047, 2522301, 7051895, 19715891, 55124449, 154123101, 430912643, 1204794989, 3368504981, 9418046333, 26332052309, 73622187095, 205841375745, 575515014243

Offset

1,2

Comments

Column 3 of A183386.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 6*a(n-3) - 13*a(n-4) + 3*a(n-5) - 2*a(n-6) + 6*a(n-7) + 4*a(n-8) + 5*a(n-9) - 4*a(n-10) - 2*a(n-11).

Empirical g.f.: x*(1 + 2*x - 2*x^2)*(1 - x - x^2 - x^3 - x^5 + 3*x^6 + x^7 + x^8) / (1 - 4*x + 4*x^2 - 6*x^3 + 13*x^4 - 3*x^5 + 2*x^6 - 6*x^7 - 4*x^8 - 5*x^9 + 4*x^10 + 2*x^11). - Colin Barker, Mar 28 2018

Example

Some solutions for 5 X 3:
..0..0..1....0..1..0....0..0..1....0..1..0....0..1..1....0..1..0....0..1..0
..1..1..0....1..0..1....1..1..0....0..1..0....1..0..0....1..0..1....0..1..1
..0..1..0....0..1..0....0..0..1....1..1..0....0..1..1....1..0..1....1..0..0
..0..1..0....1..1..0....1..1..0....0..0..1....1..0..0....0..1..0....0..1..1
..0..1..0....0..0..1....0..0..1....1..1..0....0..1..1....0..1..0....1..0..0

Crossrefs

Cf. A183386.

Sequence in context: A237642 A059508 A084817 * A100965 A001632 A234511

Adjacent sequences: A183379 A183380 A183381 * A183383 A183384 A183385

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved